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Journal of Applied Mathematics
Volume 2012, Article ID 401960, 20 pages
http://dx.doi.org/10.1155/2012/401960
Research Article

Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications

1Department of Mathematics, Cangzhou Normal University, Cangzhou 061001, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 27 November 2011; Accepted 15 December 2011

Academic Editor: Yonghong Yao

Copyright © 2012 Sumei Ai and Yongfu Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, (3) two examples of uniformly closed countable families of nonlinear mappings and applications, (4) an example which is hemirelatively nonexpansive mapping but not weak relatively nonexpansive mapping, and (5) an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping. Therefore, the results of this paper improve and extend the results of Plubtieng and Ungchittrakool (2010) and many others.